 
Summary: Partially wellordered closed sets of permutations
M. D. Atkinson
Department of Computer Science
University of Otago, New Zealand
M. M. Murphy
School of Mathematics and Statistics
University of St Andrews, UK
N. Ruskuc
School of Mathematics and Statistics
University of St Andrews, UK
Abstract
It is known that the \pattern containment" order on permutations
is not a partial wellorder. Nevertheless, many naturally dened sub
sets of permutations are partially wellordered, in which case they have
a strong nite basis property. Several classes are proved to be partially
wellordered under pattern containment. Conversely, a number of new
antichains are exhibited that give some insight as to where the boundary
between partially wellordered and not partially wellordered classes lies.
Keywords Permutation, pattern containment, involvement, nite basis, partial
wellorder
